The field of the invention is magnetic resonance imaging (“MRI”). More particularly, the invention relates to magnetic resonance elastography (“MRE”).
Magnetic resonance elastography (“MRE”) is a phase-contrast MRI technique that is capable of spatially resolving the shear stiffness of biological tissues. MRE provides a sensitive metric for the detection of both benign and malignant processes in tissues such as those in the breast, prostate, heart, skeletal muscle, brain, and liver. These applications of MRE have been applied to organs in which the signal-to-noise ratio (“SNR”) is generally considered to be high, both in terms of the magnitude of the MRE signal as well as the phase into which the shear wave displacements are encoded. In contrast, MRE of tissues such as the lung is uniquely challenging due in large part to the decreased SNR of both the magnitude and phase of conventional proton MRE images. This decrease in SNR is due to the decreased physical density of the lung compared to solid organs, and because of the ultra-short transverse relaxation time, T2*, of lung parenchyma. Decreased physical density reduces the number of protons that contribute to the net signal within each voxel, and hence decreased SNR. The ultra-short T2* of lung parenchyma, which is of the order of 1-2 milliseconds, means that significant signal decay occurs during the typical echo time used to acquire the MR signal using conventional pulse sequences. This rapid decay results in further signal loss and SNR degradation. The decrease in SNR is also further exacerbated with increasing inflation pressure, which results in decreased physical density and increased susceptibility-induced signal loss.
Many techniques to calculate shear modulus from MRE wave displacement data have been described, with perhaps the most commonly used being direct inversion of the Helmholtz equation. In moderate-to-high SNR data sets, various inversion methods have been shown to accurately calculate the shear stiffness of tissue like materials; however, as the SNR of the MRE data decreases, direct inversion and other inversion methods can underestimate the value of the shear stiffness, particularly in less elastic materials in which the shear wavelength becomes large compared to the object dimensions.
A common method to calculate the shear stiffness of biological tissue that is more robust to noise is local frequency estimation (“LFE”). This method estimates the local spatial frequency, and hence wavelength and wave speed, over a range of several frequency scales. The shear stiffness is then calculated based on the relationship μ=ρc2 between the shear modulus, μ, of a purely elastic material, the density of the material, ρ, and the shear wave speed, c. This formula assumes no attenuation, and hence the shear stiffness is an effective quantity; that is, the stiffness of a purely elastic material that would give the observed wavelength.
The problem of low SNR becomes particularly important in the case of measuring mechanical properties of the lung. The lung is a relatively inelastic organ in which the density is typically one third that of solid organs and which varies throughout the respiratory cycle due to changes in tidal lung volume. The SNR of MRE lung data is very low due to the lung's low physical density and ultra short T2* value. Additionally, a decrease in SNR with increasing lung volume can introduce a pressure-dependent bias in the MRE estimate of shear stiffness, with shear stiffness being increasingly underestimated as lung volume, and hence transpulmonary pressure (“Ptp”), increases. While it is generally appreciated that lung stiffness is a linear function of Ptp with a slope approximately equal to 0.7 (when Ptp is measured in centimeters of water), underestimation of shear stiffness with increasing Ptp due to decreased SNR will result in an underestimate of this slope. Deviation from the true value of the slope, and hence shear stiffness, will introduce errors that could be misinterpreted as indicative of some disease process, or will affect the diagnostic sensitivity and specificity of MRE-based estimates of shear stiffness.
It would therefore be desirable to provide a method for MRE that is robust to low SNR data sets, such as those acquired from lung tissue.